An 18-kg child is riding in a child-restraint chair, securely fastened to the seat of a car (Fig. 4–69). Assume the car has speed 45 km/h when it hits a tree and is brought to rest in 0.20 s. Assuming constant deceleration during the collision, estimate the net horizontal force F that the straps of the restraint chair exert on the child to hold her in the chair. <IMAGE>

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 $\overrightarrow{F}$ whose direction makes an angle of $30.0$° with the ramp (Fig. E$4.4$). How large a force $\overrightarrow{F}$ is necessary for the component $F_x$ parallel to the ramp to be $90.0$ N?

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II) Using focused laser light, optical tweezers can apply a force of about 10 pN (piconewtons) to a 1.0-μm-diameter polystyrene bead, which has a density about equal to that of water: a volume of 1.0 cm³ has a mass of about 1.0 g. Estimate the bead's acceleration in g's.

(II) A high-speed 14-car Italian train has a mass of 640 metric tons (640,000 kg). It can exert a maximum force of 400 kN horizontally against the tracks, whereas at maximum constant velocity (300 km/h), it exerts a force of about 150 kN. Calculate a) its maximum acceleration, and (b) estimate the total force of friction and air resistance at top speed.

Superman must stop a 120-km/h train in 150 m to keep it from hitting a stalled car on the tracks. If the train's mass is 3.6 x 10⁵ kg, how much force must he exert? Compare to the weight of the train (give as %). How much force does the train exert on Superman?

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. 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. 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. What was its acceleration (in m/s² and in g's), assumed to be constant, during the crash?