7. Friction, Inclines, Systems

A 4.0-kg box sits on a frictionless inclined plane that makes a 21° angle with the horizontal. It is held in place by a cord parallel to the plane. Calculate the tension in the cord.

An $8.00$-kg block of ice, released from rest at the top of a $1.50$-m-long frictionless ramp, slides downhill, reaching a speed of $2.50$ m/s at the bottom. What is the angle between the ramp and the horizontal?

A 4000 kg truck is parked on a 15° slope. How big is the friction force on the truck? The coefficient of static friction between the tires and the road is 0.90.

A rifle with a barrel length of 60 cm fires a 10 g bullet with a horizontal speed of 400 m/s. The bullet strikes a block of wood and penetrates to a depth of 12 cm. How long does it take the bullet to come to rest?

A 2.0 kg block on a horizontal, frictionless surface is connected by a massless spring and a massless, frictionless pulley to a hanging mass. For what value of the hanging mass does the block accelerate at 1.5 m/s²?

(II) A block is given an initial speed of 5.2m/s up the 22.0° plane shown in Fig. 4–45. How much time elapses before it returns to its starting point? Ignore friction.

Consider the system shown in Fig. 4–68 with m_A = 8.2kg and m_B = 11.5kg. The angles θ_A = 59° and θ_B = 32°. In the absence of friction, what force $\overrightarrow{F}$ would be required to pull the masses at a constant velocity up the fixed inclines?

A parent pulls his child in a wagon across a floor. The child and wagon have a combined mass of 35 kg. The wagon handle is inclined at 55° to the horizontal, and the child and wagon (whose wheels are nearly frictionless) are accelerating at 0.42m/s². With what force is the parent pulling on the wagon handle?

In the design of a supermarket, there are to be several ramps connecting different parts of the store. Customers will have to push grocery carts up the ramps and it is desirable that this not be too difficult. The engineer has done a survey and found that almost no one complains if the force required is no more than 23 N. Ignoring friction, at what maximum angle θ should the ramps be built, assuming a full 25-kg cart?

Three mountain climbers who are roped together in a line are ascending an icefield inclined at 29° to the horizontal (Fig. 4–67). The last climber slips, pulling the second climber off his feet. The first climber is able to hold them both. If each climber has a mass of 75 kg, calculate the tension in each of the two sections of rope between the three climbers. Ignore friction between the ice and the fallen climbers.

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Consider the system shown in Fig. 4–68 with m_A = 8.2kg and m_B = 11.5kg. The angles θ_A = 59° and θ_B = 32°. In the absence of $\overrightarrow{F}$, what is the tension in the string?

A car starts rolling down a 1-in-4 hill (1-in-4 means that for each 4 m traveled along the road, the elevation change is 1 m). How fast is it going when it reaches the bottom after traveling 55 m? Ignore friction.

A city planner is working on the redesign of a hilly portion of a city. An important consideration is how steep the roads can be so that even low-powered cars can get up the hills without slowing down. A particular small car, with a mass of 920 kg, can accelerate on a level road from rest to 21m/s (75km/h) in 14.5 s. Using these data, calculate the maximum steepness of a hill.