Q: A 35 kg board is suspended horizontally by two wires, and a 3.0 kg weight is attached at one end. What is the tension in the wire at the end with the weight? (Assume the board is uniform and the wires are vertical.)

$$T = \frac{(35\,\mathrm{kg} \times 9.8\,\mathrm{m/s^2$})}{2} + 3.0\,\mathrm{kg} \times 9.8\,\mathrm{m/s^2$}$$

Q: A 3.0 m long diving board is held up by a downward force $$F_2$$ and an upward force $$F_1 at $$the right end. The board is uniform and has a mass of 28 kg. A diver of mass 75 kg stands at the far right end. What is the magnitude of the upward force $$F_1$$?

$$F_1$$ = \frac{28\,\mathrm{kg} \times 9.8\,\mathrm{$$m/s^2$$} \times 1.5\,\mathrm{m} + 75\,\mathrm{kg} \times 9.8\,\mathrm{$$m/s^2$$} \times 3.0\,\mathrm{m}}{3.0\,\mathrm{m}}$$

Q: A pitched baseball (0.145 kg) with speed 45.0 m/s is hit by a bat so that its speed becomes 55.0 m/s in the opposite direction. If the contact time is 2.00 ms, what is the average force applied to the ball?

$$F_{avg} = \frac{0.145\,\mathrm{kg} \times (55.0\,\mathrm{m/s} - (-45.0\,\mathrm{m/s}))}{0.002\,\mathrm{s}}$$

Q: A skater of mass 70 kg moving to the right at 20.0 m/s collides with another skater of mass 65 kg moving to the left at 25.0 m/s. What is their final velocity if they hold on to each other after the collision?

$$v_f = \frac{70\,\mathrm{kg} \times 20.0\,\mathrm{m/s} + 65\,\mathrm{kg} \times (-25.0\,\mathrm{m/s})}{70\,\mathrm{kg} + 65\,\mathrm{kg}}$$

Q: An open-topped freight car of mass 24,000 kg is coasting on a frictionless, level track at 4.0 m/s when hard rain begins falling straight down. What is the speed of the car after it has collected 3,000 kg of rainwater?

$$v_f = \frac{24,000\,\mathrm{kg} \times 4.0\,\mathrm{m/s}}{24,000\,\mathrm{kg} + 3,000\,\mathrm{kg}}$$

Q: Two coupled cars on an air track are moving to the right at 1.2 m/s when they separate by a spring. The force on one car (mass 0.40 kg) ends up moving at 1.5 m/s to the left. What is the final velocity of the back car (mass 0.60 kg)?

$$v_{f,2} = \frac{(0.40\,\mathrm{kg} \times 1.2\,\mathrm{m/s}) - (0.40\,\mathrm{kg} \times (-1.5\,\mathrm{m/s}))}{0.60\,\mathrm{kg}}$$

Q: A golf ball is hit off the tee with a driver that causes an average force on the ball of 450 N for a time of 0.065 s. If the mass of the ball is 0.046 kg, what is the final speed of the ball after it has been hit?

$$v_f = \frac{450\,\mathrm{N} \times 0.065\,\mathrm{s}}{0.046\,\mathrm{kg}}$$

Q: A 0.145 kg baseball is pitched at 45.0 m/s and hit so that it moves at 55.0 m/s in the opposite direction. What is the change in momentum of the ball?

$$\Delta p = 0.145\,\mathrm{kg} \times (55.0\,\mathrm{m/s} - (-45.0\,\mathrm{m/s}))$$

Question 1

A 35 kg board is suspended horizontally by two wires, and a 3.0 kg weight is attached at one end. What is the tension in the wire at the end with the weight? (Assume the board is uniform and the wires are vertical.)

Accepted Answer

$$T = \frac{(35\,\mathrm{kg} 	imes 9.8\,\mathrm{m/s^2$})}{2} + 3.0\,\mathrm{kg} 	imes 9.8\,\mathrm{m/s^2$}$$

Question 2

A 3.0 m long diving board is held up by a downward force $$F_2$$ and an upward force $$F_1 at $$the right end. The board is uniform and has a mass of 28 kg. A diver of mass 75 kg stands at the far right end. What is the magnitude of the upward force $$F_1$$?

Accepted Answer

$$F_1$$ = \frac{28\,\mathrm{kg} 	imes 9.8\,\mathrm{$$m/s^2$$} 	imes 1.5\,\mathrm{m} + 75\,\mathrm{kg} 	imes 9.8\,\mathrm{$$m/s^2$$} 	imes 3.0\,\mathrm{m}}{3.0\,\mathrm{m}}$$

Question 3

A spring scale is used to measure the weight of an object. The spring is stretched 8.5 cm and the force meter reads 5.6 N. If the spring constant is 71 N/m, what is the mass of the object?

Accepted Answer

$$m = \frac{5.6\,\mathrm{N}}{9.8\,\mathrm{m/s^2$}}$$

Question 4

A pitched baseball (0.145 kg) with speed 45.0 m/s is hit by a bat so that its speed becomes 55.0 m/s in the opposite direction. If the contact time is 2.00 ms, what is the average force applied to the ball?

Accepted Answer

$$F_{avg} = \frac{0.145\,\mathrm{kg} 	imes (55.0\,\mathrm{m/s} - (-45.0\,\mathrm{m/s}))}{0.002\,\mathrm{s}}$$

Question 5

A skater of mass 70 kg moving to the right at 20.0 m/s collides with another skater of mass 65 kg moving to the left at 25.0 m/s. What is their final velocity if they hold on to each other after the collision?

Accepted Answer

$$v_f = \frac{70\,\mathrm{kg} 	imes 20.0\,\mathrm{m/s} + 65\,\mathrm{kg} 	imes (-25.0\,\mathrm{m/s})}{70\,\mathrm{kg} + 65\,\mathrm{kg}}$$

Question 6

An open-topped freight car of mass 24,000 kg is coasting on a frictionless, level track at 4.0 m/s when hard rain begins falling straight down. What is the speed of the car after it has collected 3,000 kg of rainwater?

Accepted Answer

$$v_f = \frac{24,000\,\mathrm{kg} 	imes 4.0\,\mathrm{m/s}}{24,000\,\mathrm{kg} + 3,000\,\mathrm{kg}}$$

Question 7

Two coupled cars on an air track are moving to the right at 1.2 m/s when they separate by a spring. The force on one car (mass 0.40 kg) ends up moving at 1.5 m/s to the left. What is the final velocity of the back car (mass 0.60 kg)?

Accepted Answer

$$v_{f,2} = \frac{(0.40\,\mathrm{kg} 	imes 1.2\,\mathrm{m/s}) - (0.40\,\mathrm{kg} 	imes (-1.5\,\mathrm{m/s}))}{0.60\,\mathrm{kg}}$$

Question 8

A golf ball is hit off the tee with a driver that causes an average force on the ball of 450 N for a time of 0.065 s. If the mass of the ball is 0.046 kg, what is the final speed of the ball after it has been hit?

Accepted Answer

$$v_f = \frac{450\,\mathrm{N} 	imes 0.065\,\mathrm{s}}{0.046\,\mathrm{kg}}$$

Question 9

A spring scale reads 7.4 N when stretched by an object. If the spring constant is 71 N/m, how far is the spring stretched?

Accepted Answer

$$x = \frac{7.4\,\mathrm{N}}{71\,\mathrm{N/m}}$$

Question 10

A 0.145 kg baseball is pitched at 45.0 m/s and hit so that it moves at 55.0 m/s in the opposite direction. What is the change in momentum of the ball?

Accepted Answer

$$\Delta p = 0.145\,\mathrm{kg} 	imes (55.0\,\mathrm{m/s} - (-45.0\,\mathrm{m/s}))$$

Question 11

A freight car of mass 24,000 kg is moving at 4.0 m/s and collects 3,000 kg of rainwater. What type of collision does this scenario best represent?

Accepted Answer

Perfectly inelastic collision

Question 12

A diver of mass 75 kg stands at the end of a 3.0 m long board of mass 28 kg. What is the torque about the left end due to the diver?

Accepted Answer

$$	au = 75\,\mathrm{kg} 	imes 9.8\,\mathrm{m/s^2$} 	imes 3.0\,\mathrm{m}$$

Question 13

A spring scale is used to measure the weight of an object. If the spring constant is 71 N/m and the scale reads 5.6 N, what is the extension of the spring?

Accepted Answer

$$x = \frac{5.6\,\mathrm{N}}{71\,\mathrm{N/m}}$$

Question 14

A 0.40 kg car and a 0.60 kg car are coupled and move at 1.2 m/s. After separation, the 0.40 kg car moves at 1.5 m/s to the left. What is the total momentum before separation?

Accepted Answer

$$p_{total} = (0.40\,\mathrm{kg} + 0.60\,\mathrm{kg}) 	imes 1.2\,\mathrm{m/s}$$

Question 15

A 0.046 kg golf ball is hit with an average force of 450 N for 0.065 s. What is the impulse delivered to the ball?

Accepted Answer

$$J = 450\,\mathrm{N} 	imes 0.065\,\mathrm{s}$$

Physics Study Notes: Forces, Newton's Laws, and Momentum

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