Question # 1 : What is the maximum acceleration a car can undergo if the coefficient of static friction between the tires and the ground is 0.82?

Question # 2 : A 1.5-kg block rests on top of a 7.5kg block. The cord and pulley have negligible mass, and there is no significant friction anywhere.

Part a) What force F must be applied to the bottom block so the top block accelerates to the right at 2.9 m/s^2 ?

Part b) What is the tension in the connecting cord?

1. Fnet=ma=Fs

Fnet=ma=usFn
Fnet=ma=usmg
mass canceles
a=usg

2. not a very good visual description, cant figure out what you mean. draw pictures. use a free body diagram

Q1:

The car moves forward by the reaction force from the ground, produced due to friction between tires and road. According to the Newton’s 3rd law
F12 = F21
F(net)max = F(friction)max
m•a = k• m•g
a = k• g = 0.82•9.8 = 8.04 m/s^2.Q2:
m1 =1.5 kg, m2 = 7.5 kg, a=2.9 m/s²
(a) The horizontal projections of the equations of motion for each block are
m1•a = T,
m2•a = T-F,
F = (m1+m2) •a = (1.5+7.5) •2.9 = 26.1 N,
(b) T= m2•a - F= 7.5•2.9 – 26.1 = 4.35 N.

To answer these questions, we will use Newton's second law of motion, which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration (F = ma).

Question #1:
The maximum acceleration a car can undergo is determined by the coefficient of static friction between the tires and the ground. The formula to calculate the maximum acceleration is a = μg, where μ is the coefficient of static friction and g is the acceleration due to gravity (approximately 9.8 m/s^2).

To find the maximum acceleration, substitute the given coefficient of static friction into the formula: a = 0.82 * 9.8.

Question #2:
Part a) To find the force F required to accelerate the top block at 2.9 m/s^2, we need to consider the forces acting on the system. In this case, the force F is applied to the bottom block, causing it to accelerate to the right. As there is no significant friction, the only horizontal force acting on the bottom block is the tension in the connecting cord.

Using Newton's second law, we can write the equation: F - T = m₁a₁, where F is the applied force, T is the tension in the cord, m₁ is the mass of the bottom block, and a₁ is its acceleration. Since the top block is accelerating to the right, the bottom block will also accelerate to the right with the same acceleration.

Part b) To find the tension in the connecting cord, we need to analyze the forces acting on the top block. In this case, the only force acting on the top block is the force of gravity (its weight). Therefore, the tension in the cord must be equal to the weight of both blocks combined.

Using Newton's second law, we can write the equation: T - m₂g = m₂a₂, where T is the tension in the cord, m₂ is the mass of the top block, g is the acceleration due to gravity, and a₂ is the acceleration of the top block (2.9 m/s^2).

Solve the equations simultaneously to find the force F in part a) and the tension T in part b).