A 9 kg hanging weight is connected by a string over a pulley to a 5 kg block sliding on a flat
table. If the coefficient of sliding friction is 0.2, find the tension in the string.
To find the tension in the string, we need to analyze the forces acting on both objects and set up an equation using Newton's second law.
Let's break it down step by step:
Step 1: Identify the forces acting on the hanging weight and the sliding block.
For the hanging weight:
- Force due to gravity (weight, W): W = m1 * g, where m1 is the mass of the hanging weight and g is the acceleration due to gravity (9.8 m/s^2).
For the sliding block:
- Force due to gravity (weight, W): W = m2 * g, where m2 is the mass of the sliding block and g is the acceleration due to gravity (9.8 m/s^2).
- Force of friction (Ffriction): Ffriction = μ * N, where μ is the coefficient of sliding friction and N is the normal force. The normal force is equal to the weight of the block in this case.
Step 2: Calculate the normal force acting on the sliding block.
Since the block is on a flat table and not accelerating vertically, the normal force is equal to the weight of the block.
N = m2 * g
Step 3: Set up the equation using Newton's second law.
For the hanging weight:
Force upwards - Force downwards = net force
T - W = m1 * a
For the sliding block:
Force to the right - Force to the left = net force
Ffriction = m2 * a
Step 4: Substitute the relevant values and equations into the set-up equation.
For the hanging weight:
T - m1 * g = m1 * a
For the sliding block:
μ * N = m2 * a
Step 5: Solve the set of equations simultaneously to find the acceleration (a).
Substitute N = m2 * g into the equation for the sliding block:
μ * m2 * g = m2 * a
Simplify: μ * g = a
Substitute a = μ * g into the equation for the hanging weight:
T - m1 * g = m1 * (μ * g)
Step 6: Solve for T, the tension in the string.
T - m1 * g = m1 * (μ * g)
T = m1 * μ * g + m1 * g
Step 7: Substitute the given values and calculate T.
T = 9 kg * 0.2 * 9.8 m/s^2 + 9 kg * 9.8 m/s^2
T ≈ 17.64 N
Therefore, the tension in the string is approximately 17.64 Newtons.
To find the tension in the string, we need to calculate the forces acting on the system.
For the hanging weight:
The force acting on the weight is equal to its weight, which can be calculated using the formula:
Weight = mass × acceleration due to gravity
Weight = 9 kg × 9.8 m/s² (acceleration due to gravity) = 88.2 N
For the sliding block:
The force of friction acting on the block can be calculated using the formula:
Force of friction = coefficient of sliding friction × normal force
The normal force is the force exerted by the table on the block and is equal to the weight of the block. So the normal force can be calculated as:
Normal force = mass × acceleration due to gravity
Normal force = 5 kg × 9.8 m/s² (acceleration due to gravity) = 49 N
Plugging in the values:
Force of friction = 0.2 × 49 N = 9.8 N
Since the string is connected between the hanging weight and the sliding block over a pulley, the tension in the string is the same throughout the system.
Tension in the string = Force acting on the sliding block - Force of friction
Tension in the string = 88.2 N - 9.8 N = 78.4 N
Therefore, the tension in the string is 78.4 N.
9*g - T = 9*a
T - 5*g*0.2 = 5*a
8*g = 14 a
a = 5/7 g
T = 9 g - 9 a = 9 g - 45/7 g
= 18/7 g Newtons