Three objects are connceted by a massless wires over a frictionless pulley. The right side of the pulley wire is connected to a 15kg block and right below that is a 10kg block on the bottom of the wire. The tension in the wire connecting the 10kg and 15kg objects is measured to be 133 N. What is the weight of the unknown mass on the left side of the pulley or other side of the pulley.
52.8
To find the weight of the unknown mass on the left side of the pulley, we need to use the principle of equilibrium.
1. Start by considering the forces acting on each block. For the 15kg block on the right side, the only force acting on it is its weight (W = m * g), where m is the mass of the block (15kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. For the 10kg block on the left side, there are two forces acting on it: the tension in the wire (133N) and its weight.
3. Since the objects are connected by a massless wire over a frictionless pulley, the tension in the wire is the same on both sides of the pulley.
4. Set up an equation using the principle of equilibrium: the sum of the forces on each side should be equal.
For the 15kg block on the right side:
W = 15kg * 9.8 m/s^2 = 147N
For the 10kg block on the left side:
Tension + Weight = 133N + Weight
5. Since the tension in the wire is the same on both sides (133N), we can rewrite the equation as:
133N + Weight = 133N + Weight
6. Simplify the equation:
Weight - Weight = 133N - 133N
0 = 0
7. This means that the weight of the unknown mass on the left side of the pulley is 0. The unknown mass could be either 0kg or an object with negligible weight.
To find the weight of the unknown mass on the other side of the pulley, we need to use the principle of equilibrium. Since the system is at rest, the sum of the forces in the vertical direction must be zero.
Let's break down the forces acting on each object in the system:
For the 15kg block:
1. Weight (W1): It can be calculated as the mass (m1) multiplied by the acceleration due to gravity (g). So, W1 = m1 * g.
For the 10kg block:
1. Weight (W2): It can be calculated as the mass (m2) multiplied by the acceleration due to gravity (g). So, W2 = m2 * g.
2. Tension force (T1): The tension in the wire connecting the 10kg and 15kg objects is given as 133 N.
In this system of connected objects, the tension in the wire connecting them (133 N) is the same as the weight of the 10kg block (W2). So, T1 = W2.
Now, let's write the equation for the sum of the forces in the vertical direction:
T1 - W1 - W2 = 0
Substituting T1 = 133 N and W2 = m2 * g, we have:
133 N - W1 - m2 * g = 0
Since we are interested in the weight of the unknown mass (W1), we rearrange the equation:
W1 = 133 N - m2 * g
Substituting the given values of m2 = 10 kg and g = 9.8 m/s^2, we can calculate W1:
W1 = 133 N - 10 kg * 9.8 m/s^2
W1 = 133 N - 98 N
W1 = 35 N
Therefore, the weight of the unknown mass on the other side of the pulley is 35 N.