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Physics Reviewer

Problem 1

Vectors A, B, and C satisfy the vector equation Vector A + Vector B = Vector C and their magnitude are related by the scalar equation A² + B² = C². How is vector A oriented with respect to Vector B? Explain your answer.

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Problem 2

Are two vectors with the same magnitude necessarily equal? Explain your answer.

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Problem 3

Assuming a car has gasoline consumption of 6 km/liter of gasoline. Its average speed is 60 km/hour. How far can a car travel in one and one half hours?

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Problem 4

A straight track is 1600 meter in length. A runner begins at the starting line, runs due east for the full length of the track, turns around, and runs halfway back. The time for this run is five minutes. What is the runner's average velocity, and what is the average speed?

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Problem 5

A plane starts from rest. The plane accelerates down the runway and at T=29 seconds attains a velocity of -260 km/hour. Determine the average acceleration of the plane in m/s² ?

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Problem 6

The spacecraft shown below has an initial velocity component of V_ox = - 22 m/s and an acceleration component of A _x = -24 m/s ² and V_oy = + 14 m/s and A _y = + 12 m/s ². Calculate the final displacement in x and y axis and the final velocity component, V _x and V _y after 7 seconds the spacecraft was initially observed.

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Problem 7

An airplane moving horizontally with a constant velocity of -115 m/s at an altitude of 1050 meter. The direction of airplane to the right have been chosen as the positive direction. The plane release a crate box that falls to the ground along a curved trajectory. Ignoring air resistance, determine the time required for the crate box to hit the ground.

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Problem 8

A projectile is launched from and return to ground level as shown below. Air resistance is neglected. The horizontal range of the projectile is R= 1200 meters and the horizontal component of the launch velocity is V_ox = 25 m/s. Find the vertical component of V_oy of the launch velocity.

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Problem 9

Two people pushing a stalled car. The mass of the car is 1850 kg. One person applies a force of 300 Newton (N) to the car, while the other applies a force of 200 Newton (N). Both forces act in the same direction. A third force of 400 N also acts on the car, but in a direction opposite to that in which the two people are pushing. This third force is due to road frictional force. Find the acceleration of the car.

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Problem 10

A man is paddling his boat (mass of man and boat = 1500 kg). By paddling, he causes an average force designated as variable letter P (paddling force) of 17 Newton (N) to applied to the boat in a direction due east. The wind also exerts a force W (wind force) on the boat. This wind force, W has a magnitude of 15 Newton (N) and points 60 degree north of east. Ignoring any resistance from the water, find the x and y component of the boat's acceleration.

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Problem 11

An astronaut exerts a force of P = 40 N on the spacecraft. The mass of the spacecraft is 11,500 kg and the mass of the astronaut is 90 kg. Find the acceleration of spacecraft and the astronaut.

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Problem 12

A traction device is use in a foot injury. The weight of 3 kg. object creates a tension in the rope that passes around the pulleys. The foot pulley is kept in equilibrium because the foot also applies a force, F to it. This force arises due to the Newton's 3rd law of motion, opposite reaction to the pulling effect of forces T1 and T2. Ignoring the weight of the foot, find the magnitude of force, F.

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Problem 13

The engine weight is 3,150 Newton (N). This engine is being raised to certain height. Find the tension T-1 in the supporting cable and the tension T-2.

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Problem 14

A jet plane is flying with a constant speed a long a straight line, at an angle of 30° above the horizontal. The plane has a weight of W = 87,200 Newton (N) and its engines provide a forward thrust T = 105,000 Newton (N). In addition, the lift force, L (directed perpendicular to the wings) and the force R, air resistance (directed opposite to the motion) act on the plane. Find the lift force, L, and the air resistance force, R.

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Problem 15

The achilles tendon exerts a force of magnitude, F = 750 Newton (N). Determine the torque (magnitude and direction) of this force about the ankle joint, which is located 0.03 meter (m) away from the heel point, P.

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Problem 16

A square, 0.50 m on a side, is mounted so that it can rotate about an axis that passes through the center of the square. The axis is perpinducular to the plane of the square. A force, F 15 N lies in this plane and is applied to the square. What is the magnitude of the maximum torque that such force could produce?

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Problem 17

You are installing a new spark plug in your car, and the manual specifies that it be tightened to a torque that has magnitude of 45 N*m. Use the sketch below to determine the force, F, that you must exert on the wrench.

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Problem 18

Find the work done by a 50 N force in pulling the suitcase at an angle of 60° for a distance of 75 m.

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Problem 19

A 1,200 kg car starting form rest, accelerates for 5 s. The magnitude of the acceleration is a = 4.6 m/s². Determine the average power generated by the net force that accelerate the car in horspower, hp.

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Problem 20

The space probe was launched and its mass was 500 kg. Consider the probe is traveling at initial speed of V_o = 270 m/s. No forces act on it except the 56 m N thrust of its engine. The external engine thrust force, T, is directed parallel to the displacement of 3 x 10⁹ m. Determine the final speed of the probe, assuming that the mass remains constant.

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Problem 21

A baseball (mass, m=0.15 kg) has an initial velocity, V_o = -38 m/s as it approaches a bat. Selected the direction of the baseball approach as the negative direction. The bat applies an average force, F_ave, that is much larger than the weight of the baseball, and the ball departs from the bat with a final velocity of V_f = +58 m/s.

a) Compute the impulse applied to the ball by the bat.

b) Assuming that the time of contact is
∆ t = 1.6 x10^-3 s. Find the average force exerted on the ball by the bat.

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Problem 22

Car 1 has a mass of m₁ = 70 x 10³ kg and moves at a velocity of V₀₁ = +0.80 m/s. The freight operator decided to couple a Car 2 to Car 1 at the switching yard. Car 2 has a mass m₂ =90 x 10³ kg and it is running at velocity of V₀₂ = +1.3 m/s to overtakes Car 1 and to couple to it. Neglecting friction, find the common velocity, V, of the cars after they become coupled.

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Problem 23

Starting from rest, two skater "push off" against each other on smooth ice, where friction is negligible. The woman mass, m₁ = 50 kg. and the man mass, m₂ = 90 kg. After their "push off" the woman moves away with a velocity of V_f1 = +2.5 m/s (velocity to the right is selected as positive). Find the recoil velocity of the man.

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Problem 24

Suppose the pressure acting on the back of a swimmer is 1.4 x 10⁵ Pa near the bottom of the pool. The surface area of the swimmer's back is 0.85 m². Determine the magnitude of the force that acts on the swimmer's back.

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Problem 25

Blood in the arteries can be treated as a static fluid. Estimate how much blood pressure, P2, at the foot in the anterior tibial artery exceeds the blood pressure, P1, in the aorta at the heart;

a) when the body is reclining horizontally - see sketch 1 below.

b) when the body is standing. see sketch 2 below.

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Problem 26

A concrete sidewalk is constructed between two building on a day when the temperature is 25 ° C. The sidewalk consists of two slabs, each three meters in length and of negligible thickness. As the temperature rises to 40 ° C, the slabs expand, but no space is provided for thermal expansion. The building do not move, so the slabs buckle upward. Determine the change in length of each slab associated with this temperature change.

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Problem 27

In half hour, a 50 kg jogger can generate 9.0 x 10⁵ J of heat. This heat is removed from the jogger's body by a variety of means, including the body's own temperature-regulating mechanisms. If the heat were not removed, how much would the body temperature increase?

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How can IN-V-BAT-AI be used in classrooms ?

The IN-V-BAT-AI solution can be a valuable tool in classrooms, enhancing both teaching and learning experience. Here are some ways it can be utilized:

⋆ Personalized Learning : By storing and retrieving knowledge in the cloud, students can access tailored resources and revisit concepts they struggle with, ensuring a more individualized learning journey.

⋆ Memory Support : The tool helps students recall information even when stress or distractions hinder their memory, making it easier to retain and apply knowledge during homework assignments or projects.

⋆ Bridging Learning Gaps : It addresses learning loss by providing consistent access to educational materials, ensuring that students who miss lessons can catch up effectively.

⋆ Teacher Assistance : Educators can use the tool to provide targeted interventions to support learning.

⋆ Stress Reduction : By alleviating the pressure of memorization, students can focus on understanding and applying concepts, fostering a deeper engagement with the material.

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