A 33.3- kg block (m1) is on a horizontal surface, connected to a 5.1- kg block (m2) by a massless string. The pulley is massless and frictionless. A force of 220.1 N acts on m1 at an angle of 32.p deg. The coefficient of kinetic friction between m1 and the surface is 0.201. Determine the upward acceleration of m2.
To determine the upward acceleration of m2, we need to follow these steps:
Step 1: Calculate the force of kinetic friction acting on m1.
The force of kinetic friction (fk) can be calculated using the formula fk = μ * N, where μ is the coefficient of kinetic friction and N is the normal force. In this case, the normal force (N) acting on m1 is equal to its weight (mg). Since the block is on a horizontal surface, the normal force is equal to the mass of m1 multiplied by the acceleration due to gravity (g).
N = m1 * g
= 33.3 kg * 9.8 m/s²
≈ 326.34 N
Now, we can calculate the force of kinetic friction:
fk = μ * N
= 0.201 * 326.34 N
≈ 65.65 N
Step 2: Calculate the net force acting on m1.
The net force (Fnet) acting on m1 is the force applied (Fapplied) minus the force of kinetic friction (fk):
Fnet = Fapplied - fk
= 220.1 N - 65.65 N
≈ 154.45 N
Step 3: Determine the acceleration of m1.
The net force (Fnet) acting on an object is equal to its mass multiplied by its acceleration (Fnet = m1 * a1). Rearranging the formula, we can solve for the acceleration:
a1 = Fnet / m1
= 154.45 N / 33.3 kg
≈ 4.64 m/s²
Note: Since the problem provided the force applied at an angle, we will calculate the horizontal component of the force applied to determine the acceleration of m1.
Fapplied (horizontal) = Fapplied * cos(θ)
= 220.1 N * cos(32°)
≈ 187.39 N
a1 = Fapplied (horizontal) / m1
= 187.39 N / 33.3 kg
≈ 5.62 m/s²
Step 4: Calculate the tension in the string.
Since the pulley is massless and frictionless, the tension in the string (T) is the same on both sides. It can be calculated using the following equation:
T = m2 * g
= 5.1 kg * 9.8 m/s²
≈ 50.08 N
Step 5: Determine the acceleration of m2.
We know that the net force acting on m2 is the difference between the tension force (T) and the force of gravity (m2 * g):
Fnet (m2) = T - m2 * g
= 50.08 N - (5.1 kg * 9.8 m/s²)
≈ 0 N
Since the net force is zero, there is no acceleration in the vertical direction for m2.
Therefore, the upward acceleration of m2 is zero.