A force of 12.7 N pulls horizontally on a 1.4-kg block that slides on a rough, horizontal surface. This block is connected by a horizontal string to a second block of mass m2 = 2.32 kg on the same surface. The coefficient of kinetic friction is µk = 0.22 for both blocks.
(a) What is the acceleration of the blocks?
F=force
a=acceleration
f=friction
u=coefficient of kinetic friction
m=mass
g=gravity (9.81m/s^2)
m1=mass of block 1
m2=mass of block 2
force of friction=um1g+um2g
=(.22)(1.4-kg)(9.81m/s^2)+(.22)(2.32-kg)(9.81m/s^2)
=(3.021)+(5.002)
=8.023N
a=fnet/m1+m2
=(Fa-Ff)/(m1+m2)
=(12.7N-8.023N)/(1.4-kg + 2.32-kg)
=2.02m/s^2
I would also appreciate help/hints for part b:
(b) What is the tension in the string?
To determine the tension in the string, you need to consider the forces acting on the second block. The tension in the string will be equal to the force experienced by the second block in the direction of the force applied by the first block (12.7 N).
The forces acting on the second block are:
1. Force due to the first block (applied force): 12.7 N
2. Force due to friction: µk * m2 * g
Since the blocks are connected by a string, they have the same acceleration (a). Therefore, you can write:
Force due to friction = µk * (m1 + m2) * g
To calculate the tension in the string, subtract the force due to friction from the force applied by the first block:
Tension in the string = Force applied by the first block - Force due to friction
Tension in the string = 12.7 N - µk * (m1 + m2) * g
Substituting the given values:
µk = 0.22
m1 = 1.4 kg
m2 = 2.32 kg
g = 9.81 m/s^2
Tension in the string = 12.7 N - 0.22 * (1.4 kg + 2.32 kg) * 9.81 m/s^2
Now you can calculate the tension in the string using this equation.