Q: A rocket expels gases at a rate of $$1300\ \mathrm{kg/s}$$ with a speed of $$4.5 \times 10^3$\ \mathrm{m/s}. $$What is the force exerted on the rocket?

$$F = 5.85 \times 10^6$\ \mathrm{N}$$

Question 1

Three arrows are shot horizontally at the same speed but at different heights above the ground. Air resistance is negligible. Rank the arrows according to the magnitude of their horizontal force $$F_x$$ acting on them. Assume they are all identical. State your reasoning.

Accepted Answer

All arrows experience the same horizontal force $$F_x$$ because air resistance is negligible and gravity acts vertically.

Question 2

Suppose that, while in a squatting position, you stand on your hands and then try to pull up on your feet with a great deal of force. Why is it not possible to lift yourself off the ground in this way?

Accepted Answer

Because the force you exert on your feet is internal to your body and does not create an external reaction force to lift you.

Question 3

A constant force of $$8.0\ \mathrm{N} is $$applied to an object, causing it to accelerate at $$8.0\ \mathrm{m/s^2$}. $$What will the acceleration be if the force is doubled?

Accepted Answer

$$a = 16\ \mathrm{m/s^2$}$$

Question 4

A man pulls an empty wagon causing it to accelerate at $$1.4\ \mathrm{m/s^2$}. $$What will the acceleration be if he pulls with the same force when the wagon contains a child whose mass triples that of the wagon?

Accepted Answer

$$a = 0.47\ \mathrm{m/s^2$}$$

Question 5

Scallops eject water from their shells to provide a thrust force. If the initial motion of a $$25\ \mathrm{g}$$ scallop speeding up to escape a predator is shown in a graph with a net force of $$0.025\ \mathrm{N}$$, how does this force compare to $$0.25	imes$$ the weight of the scallop?

Accepted Answer

The force is equal to $$0.25$$ times the weight of the scallop.

Question 6

The IKAROS spacecraft uses solar sails for propulsion. If the only force acting on a $$200\ \mathrm{kg}$$ spacecraft is $$1.12\ \mathrm{N}$$, by how much would its speed increase after $$6$$ months of flight?

Accepted Answer

$$\Delta v \approx 60\ \mathrm{m/s}$$

Question 7

A $$1000\ \mathrm{kg}$$ car traveling at $$30\ \mathrm{m/s}$$ strikes a ball at rest. If the ball has a mass of $$1.4\ \mathrm{kg}$$ and is struck at $$30\ \mathrm{m/s}$$, what is the magnitude of the force that stops the ball in $$0.015\ \mathrm{s}$$?

Accepted Answer

$$F \approx 2800\ \mathrm{N}$$

Question 8

Seat belts and air bags save lives by reducing the forces exerted on the driver and passengers in an automobile collision. If a car's speed changes from $$22\ \mathrm{m/s} to$$ $$0.35\ \mathrm{m/s} in$$ $$0.10\ \mathrm{s}$$, what is the magnitude of the force exerted by the seat belt?

Accepted Answer

$$F \approx 133000\ \mathrm{N}$$

Question 9

A horizontal rope is tied to a $$50\ \mathrm{kg}$$ box on a frictionless floor. What is the tension in the rope if the box is at rest?

Accepted Answer

$$F_T = 0\ \mathrm{N}$$

Question 10

A trampoline artist flies straight up into the air, then back down onto the trampoline, where she comes instantaneously to rest when the trampoline is fully stretched. Rank her apparent weight, from largest to smallest, at: (a) at rest, (b) just before she leaves the trampoline, (c) at the top of her flight.

Accepted Answer

Largest to smallest: (a), (b), (c)

Question 11

A box rests on the (frictionless) bed of a truck. The truck driver starts the truck and accelerates forward. The box immediately starts to slide toward the rear of the truck. Which of the following best describes the forces acting on the box?

Accepted Answer

The box is acted on by gravity and the normal force from the truck bed, but no horizontal force.

Question 12

According to Newton's third law, when you push against a wall with a force of $$60\ \mathrm{N}$$, what is the reaction force?

Accepted Answer

The wall pushes back on you with a force of $$60\ \mathrm{N} in $$the opposite direction.

Question 13

A $$68\ \mathrm{kg}$$ astronaut weighs how much on the Moon, where $$g = 1.6\ \mathrm{m/s^2$}$$?

Accepted Answer

$$F = 110\ \mathrm{N}$$

Question 14

A crate is pushed along the floor with velocity $$v_i$$ and slides a distance $$d$$ after the pushing force is removed. If the mass of the crate is doubled but the initial velocity is not changed, what happens to the distance the crate slides before stopping?

Accepted Answer

No change.

Question 15

A stone hangs by a fine thread from the ceiling, and a section of the same thread dangles from the bottom of the stone. If a person gives a sharp pull on the dangling thread, where is the thread likely to break?

Accepted Answer

Below the stone, because the force is transmitted quickly and the lower thread experiences the greatest tension.

Question 16

A rocket expels gases at a rate of $$1300\ \mathrm{kg/s}$$ with a speed of $$4.5 	imes 10^3$\ \mathrm{m/s}. $$What is the force exerted on the rocket?

Accepted Answer

$$F = 5.85 	imes 10^6$\ \mathrm{N}$$

Question 17

Which of the following best describes the advantage of 'crumple zones' in modern car design?

Accepted Answer

Crumple zones increase the time over which the collision occurs, reducing the force experienced by occupants.

Forces & Momentum: Study Notes and Problem Guide

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