6. Intro to Forces (Dynamics)

A $100\mathrm{kg}$ rock is in space, far from any planets, stars or black holes. It is moving in a straight line at a constant $\mathrm{10,000}\mathrm{m}/\mathrm{s}$ relative to our sun. What total force is required to keep it moving that fast?

An elevator is going up at a constant speed in a very tall building. Assume the only forces acting on the elevator are a downward weight force and the force of a cable pulling the elevator up. Ignore air resistance and friction. How does the magnitude of the weight force compare to the magnitude of the force of the cable?

A $10\mathrm{N}$ horizontal force is applied to a $10\mathrm{kg}$ box causing it to speed up. The force of kinetic friction is $5\mathrm{N}$. Which choice best describes the subsequent motion of the box?

A hockey puck with mass 0.160 kg is at rest at the origin (x = 0) on the horizontal, frictionless surface of the rink. At time t = 0 a player applies a force of 0.250 N to the puck, parallel to the x-axis; she continues to apply this force until t = 2.00s. (a) What are the position and speed of the puck at t = 2.00 s?

A small 8.00-kg rocket burns fuel that exerts a time-varying upward force on the rocket (assume constant mass) as the rocket moves upward from the launch pad. This force obeys the equation F = A + Bt2. Measurements show that at t = 0, the force is 100.0 N, and at the end of the first 2.00 s, it is 150.0 N. (a) Find the constants A and B, including their SI units

A 4.50-kg experimental cart undergoes an acceleration in a straight line (the x-axis). The graph in Fig. E4.13 shows this acceleration as a function of time. (b) During what times is the net force on the cart a constant?

A 4.50-kg experimental cart undergoes an acceleration in a straight line (the x-axis). The graph in Fig. E4.13 shows this acceleration as a function of time. (a) Find the maximum net force on this cart. When does this maximum force occur?

A hockey puck with mass 0.160 kg is at rest at the origin (x = 0) on the horizontal, frictionless surface of the rink. At time t = 0 a player applies a force of 0.250 N to the puck, parallel to the x-axis; she continues to apply this force until t = 2.00s. (b) If the same force is again applied at t = 5.00 s, what are the position and speed of the puck at t = 7.00 s?

A dockworker applies a constant horizontal force of 80.0 N to a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves 11.0 m in 5.00 s. (a) What is the mass of the block of ice?

A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a horizontal force with magnitude 48.0 N to the box and produces an acceleration of magnitude 2.20 m/s2, what is the mass of the box?

Due to a jaw injury, a patient must wear a strap (Fig. E4.3) that produces a net upward force of 5.00 N on his chin. The tension is the same throughout the strap. To what tension must the strap be adjusted to provide the necessary upward force?

To extricate an SUV stuck in the mud, workmen use three horizontal ropes, producing the force vectors shown in Fig. E4.2. (b) Use the components to find the magnitude and direction of the resultant of the three pulls.

To extricate an SUV stuck in the mud, workmen use three horizontal ropes, producing the force vectors shown in Fig. E4.2. (a) Find the x- and y-components of each of the three pulls.

Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is 60.0°. If Rover exerts a force of 270 N and Fido exerts a force of 300 N, find the magnitude of the resultant force and the angle it makes with Rover's rope.

A man is dragging a trunk up the loading ramp of a mover's truck. The ramp has a slope angle of 20.0°, and the man pulls upward with a force F→ whose direction makes an angle of 30.0° with the ramp (Fig. E4.4). (b) How large will the component Fy perpendicular to the ramp be then?

A man is dragging a trunk up the loading ramp of a mover's truck. The ramp has a slope angle of 20.0°, and the man pulls upward with a force F→ whose direction makes an angle of 30.0° with the ramp (Fig. E4.4). (a) How large a force F→ is necessary for the component Fx parallel to the ramp to be 90.0 N?

When jumping straight up from a crouched position, an average person can reach a maximum height of about 60 cm. During the jump, the person's body from the knees up typically rises a distance of around 50 cm. To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump. (b) Draw a free-body diagram of the person during the jump.

What is the acceleration, as a multiple of g, if this force is applied to a 110 kg bicyclist? This is the combined mass of the cyclist and the bike.

If a car stops suddenly, you feel 'thrown forward.' We'd like to understand what happens to the passengers as a car stops. Imagine yourself sitting on a very slippery bench inside a car. This bench has no friction, no seat back, and there's nothing for you to hold onto. d. Describe what happens to you as the car slows down.

On September 8, 2004, the Genesis spacecraft crashed in the Utah desert because its parachute did not open. The 210-kg capsule hit the ground at 311 km/h and penetrated the soil to a depth of 81.0 cm. (a) What was its acceleration (in m/s2 and in g's), assumed to be constant, during the crash?

An astronaut is inside a 2.25 × 106 kg rocket that is blasting off vertically from the launch pad. You want this rocket to reach the speed of sound (331 m/s) as quickly as possible, but astronauts are in danger of blacking out at an acceleration greater than 4g. (b) What force, in terms of the astronaut's weight w, does the rocket exert on her? Start with a free-body diagram of the astronaut.

An astronaut is inside a 2.25 × 106 kg rocket that is blasting off vertically from the launch pad. You want this rocket to reach the speed of sound (331 m/s) as quickly as possible, but astronauts are in danger of blacking out at an acceleration greater than 4g. (a) What is the maximum initial thrust this rocket's engines can have but just barely avoid blackout? Start with a free-body diagram of the rocket.

A light rope is attached to a block with mass 4.00 kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass m is suspended from the other end. When the blocks are released, the tension in the rope is 15.0 N. (a) Draw two free-body diagrams: one for each block.

On September 8, 2004, the Genesis spacecraft crashed in the Utah desert because its parachute did not open. The 210-kg capsule hit the ground at 311 km/h and penetrated the soil to a depth of 81.0 cm. (b) What force did the ground exert on the capsule during the crash? Express the force in newtons and as a multiple of the capsule's weight.

Problems 35, 36, 37, 38, 39, and 40 show a free-body diagram. For each: a. Identify the direction of the acceleration vector a and show it as a vector next to your diagram. Or, if appropriate, write a = 0.

FIGURE EX5.14 shows an object's acceleration-versus-force graph. What is the object's mass?

A constant force is applied to an object, causing the object to accelerate at 10 m/s². What will the acceleration be if d. The force is halved and the object's mass is doubled?

A constant force is applied to an object, causing the object to accelerate at 10 m/s². What will the acceleration be if a. The force is halved?

A single force with x-component Fₓ acts on a 2.0 kg object as it moves along the x-axis. A graph of Fₓ versus t is shown in FIGURE P5.32. Draw an acceleration graph aₓ versus t) for this object.

A single force with x-component Fₓ acts on a 500 g object as it moves along the x-axis. The object's acceleration graph aₓ versus t) is shown in FIGURE P5.30. Draw a graph of Fₓ versus t.

FIGURE EX5.8 shows an acceleration-versus-force graph for three objects pulled by rubber bands. The mass of object B is 0.20 kg. What are the masses of objects A and C? Explain your reasoning.

The 100 kg block in FIGURE EX7.24 takes 6.0 s to reach the floor after being released from rest. What is the mass of the block on the left? The pulley is massless and frictionless.

Two blocks are attached to opposite ends of a massless rope that goes over a massless, frictionless, stationary pulley. One of the blocks, with a mass of 6.0 kg, accelerates downward at 3/4g. What is the mass of the other block?