Three blocks of masses 8.2 kg, 5.88 kg, and
2.19 kg are connected by light strings that
pass over frictionless pulleys as shown in the
figure. The acceleration of the 5.88 kg block
is 2.18 m/s
2
to the left and the surfaces are rough.
The acceleration of gravity is 9.8 m/s
2
.
Find the tension in the string connecting
the 8.2 kg block suspended on the left and the
5.88 kg block on the flat surface. (Assume
the same �k for both blocks in contact with
surfaces.)
Answer in units of N
without the figure, there can be no understanding.
To find the tension in the string connecting the 8.2 kg block and the 5.88 kg block, we need to apply Newton's second law of motion to this system.
Let's break down the problem into smaller parts:
1. Finding the net force acting on the 5.88 kg block:
The net force acting on an object is given by the product of its mass and acceleration:
Net Force = Mass × Acceleration
Net Force = 5.88 kg × 2.18 m/s^2 (since the block is accelerating to the left)
Net Force = 12.82 N
2. Identifying the forces acting on the 5.88 kg block:
There are two forces acting on the 5.88 kg block: the force due to tension in the string pulling it to the right and the force of friction opposing its motion to the left. Let's call the tension force T and the force of friction f.
3. Finding the force of friction:
The force of friction is given by the equation:
Force of Friction = μk × Normal Force
where μk is the coefficient of kinetic friction and Normal Force is the force exerted by the surface on the block.
Since the surfaces are rough and the 5.88 kg block is on a flat surface, we assume the same coefficient of kinetic friction for both blocks.
4. Finding the normal force on the 5.88 kg block:
The normal force is equal to the weight of the block, which is given by:
Weight = Mass × Acceleration due to gravity
Weight = 5.88 kg × 9.8 m/s^2
Weight = 57.624 N
Therefore, the normal force is also 57.624 N.
5. Finding the force of friction:
To find the force of friction, we multiply the coefficient of kinetic friction by the normal force:
Force of Friction = μk × Normal Force
Since no value is given for the coefficient of kinetic friction, we cannot solve for the force of friction at this time.
6. Finding the tension in the string:
Since we have the net force acting on the 5.88 kg block, we can set up an equation for the forces:
Net Force = Force due to Tension - Force of Friction
12.82 N = T - f
Unfortunately, without the coefficient of kinetic friction, we cannot solve for the force of friction or determine the tension in the string connecting the blocks.