a box of mass 2kg lies on a rough horizontal floor, coefficient of friction is 0.2. A light string is attached to the box in order to pull it across the floor. If the tension in the string is T. Find the tension that must be exceeded for motion to occur if the string is 45(degrees) above the horizontal
To find the tension that must be exceeded for motion to occur, we need to consider the forces acting on the box.
1. Weight (W):
The weight of the box is the force exerted by gravity on the box and can be calculated using the formula: W = m * g, where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. Normal force (N):
The normal force is the force exerted by the floor on the box and acts perpendicular to the surface of the floor. Since the box is on a horizontal floor, the normal force is equal to the weight of the box, N = W.
3. Friction force (F):
The friction force acts parallel to the surface of the floor and opposes the motion of the box. The magnitude of the friction force can be calculated using the formula: F = μ * N, where μ is the coefficient of friction.
4. Tension force (T):
The tension force is acting on the box at an angle of 45 degrees above the horizontal.
Now, to find the tension that must be exceeded for motion to occur, we need to determine the maximum possible friction force that can be exerted on the box before it starts moving. This occurs when the applied tension force is equal to the maximum static friction force.
The maximum static friction force (F_max) can be calculated by multiplying the coefficient of friction (μ) by the normal force (N): F_max = μ * N.
Since the normal force (N) is equal to the weight of the box (W), the equation becomes: F_max = μ * W.
When the applied tension force (T) is greater than the maximum static friction force (F_max), the box will start to move.
Therefore, the tension that must be exceeded for motion to occur is T > μ * W.
Let's substitute the given values:
m = 2 kg (mass of the box)
μ = 0.2 (coefficient of friction)
θ = 45 degrees (angle of tension above the horizontal)
First, calculate the weight of the box:
W = m * g
W = 2 kg * 9.8 m/s^2
W = 19.6 N
Next, calculate the maximum static friction force:
F_max = μ * W
F_max = 0.2 * 19.6 N
F_max = 3.92 N
Therefore, the tension that must be exceeded for motion to occur is T > 3.92 N.