7. Friction, Inclines, Systems

(III) A 4.0-kg block is stacked on top of a 12.0-kg block, which is accelerating along a horizontal table at a = 5.2m/s² (Fig. 5–43). Let μ_k = μ_s = μ. If μ is only half this minimum value, what is the acceleration of the 4.0-kg block with respect to the table?

Two crates connected by a rope lie on a horizontal surface (Fig. E$5.37$). Crate A has mass $m_A$, and crate B has mass $m_B$. The coefficient of kinetic friction between each crate and the surface is $μ_k$. The crates are pulled to the right at constant velocity by a horizontal force $F$. Draw one or more free-body diagrams to calculate the following in terms of $m_A$, $m_B$, and $μ_k$: the tension in the rope connecting the blocks.

A 28.0-kg block is connected to an empty 2.00-kg bucket by a cord running over a frictionless pulley (Fig. 5–56). The coefficient of static friction between the table and the block is 0.42 and the coefficient of kinetic friction between the table and the block is 0.34. Sand is gradually added to the bucket until the system just begins to move. Calculate the mass of sand added to the bucket.

Blocks of mass m₁ and m₂ are connected by a massless string that passes over the pulley in FIGURE P12.64. The pulley turns on frictionless bearings. Mass m₁ slides on a horizontal, frictionless surface. Mass m₂ is released while the blocks are at rest. Assume the pulley is massless. Find the acceleration of m₁ and the tension in the string. This is a Chapter 7 review problem.

(III) A 4.0-kg block is stacked on top of a 12.0-kg block, which is accelerating along a horizontal table at a = 5.2m/s² (Fig. 5–43). Let μ_k = μ_s = μ. If μ is only half this minimum value, what is the acceleration of the 4.0-kg block with respect to the 12.0-kg block?

Two blocks are connected by a cord over a pulley. Block A rests on a rough tabletop. Block B has mass mB=2kg and hangs over the edge of the table. The coefficients of friction between Block A and the tabletop are μs=0.6 and μk=0.4. What is the minimum mass Block A can have to keep the system from starting to move?

(II) In Fig. 5–36 the coefficient of static friction between mass m_A and the table is 0.40, whereas the coefficient of kinetic friction is 0.30. What value(s) of m_A will keep the system moving at constant speed? [Ignore masses of the cord and the (frictionless) pulley.]

(III) A 4.0-kg block is stacked on top of a 12.0-kg block, which is accelerating along a horizontal table at a = 5.2m/s² (Fig. 5–43). Let μ_k = μ_s = μ. What minimum coefficient of friction μ between the two blocks will prevent the 4.0-kg block from sliding off?

Two crates connected by a rope lie on a horizontal surface (Fig. E$5.37$). Crate A has mass $m_A$, and crate B has mass $m_B$. The coefficient of kinetic friction between each crate and the surface is ${\mu }_k$. The crates are pulled to the right at constant velocity by a horizontal force $F$. Draw one or more free-body diagrams to calculate the following in terms of $m_A$, $m_B$, and ${\mu }_k$: the magnitude of $F$.

A small block of mass m rests on the rough, sloping side of a triangular block of mass M which itself rests on a horizontal frictionless table as shown in Fig. 5–44. If the coefficient of static friction is μ, determine the minimum horizontal force F applied to M that will cause the small block m to start moving up the incline.

Bonnie and Clyde are sliding a 300 kg bank safe across the floor to their getaway car. The safe slides with a constant speed if Clyde pushes from behind with 385 N of force while Bonnie pulls forward on a rope with 350 N of force. What is the safe's coefficient of kinetic friction on the bank floor?

Blocks of mass m₁ and m₂ are connected by a massless string that passes over the pulley in FIGURE P12.64. The pulley turns on frictionless bearings. Mass m₁ slides on a horizontal, frictionless surface. Mass m₂ is released while the blocks are at rest. Suppose the pulley has mass m_p and radius R. Find the acceleration of m₁ and the tensions in the upper and lower portions of the string. Verify that your answers agree with part a if you set m_p = 0.

A uniform cube of side ℓ rests on a rough floor. It is subjected to a steady horizontal pull F, exerted a distance h above the floor as shown in Fig. 12–85. As F is increased, the block will either begin to slide, or begin to tip over. Determine the coefficient of static friction μ_s so that: the block begins to slide rather than tip. [Hint: Where will the normal force on the block act if it tips?]

What is the acceleration of the 3.0 kg block in FIGURE CP7.55 across the frictionless table? Hint: Think carefully about the acceleration constraint.

In FIGURE CP7.54, find an expression for the acceleration of m₁. The pulleys are massless and frictionless. Hint: Think carefully about the acceleration constraint.