A 60 kg painter on a 15 kg platform. A rope attached to the platform a...
**Solution:**
Given:
- Mass of the painter, m₁ = 60 kg
- Mass of the platform, m₂ = 15 kg
- Force exerted by the painter to start, F = 400 N
(i) **Acceleration of the platform and painter:**
To find the acceleration, we need to apply Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
1. Find the total mass of the system:
- Total mass, M = m₁ + m₂ = 60 kg + 15 kg = 75 kg
2. Find the net force acting on the system:
- Net force, F_net = F - Weight of the system
- Weight of the system = (m₁ + m₂) * g, where g is the acceleration due to gravity (9.8 m/s²)
- Weight of the system = 75 kg * 9.8 m/s² = 735 N
- F_net = 400 N - 735 N = -335 N (negative sign indicates downward force)
3. Calculate the acceleration:
- F_net = M * a
- -335 N = 75 kg * a
- a = -4.47 m/s² (negative sign indicates downward acceleration)
Therefore, the acceleration of the platform and painter is -4.47 m/s², directed downward.
(ii) **Force required to attain an upward speed of 1 m/s in 1 s:**
To find the force required, we need to apply Newton's second law of motion again, using the given time interval and desired velocity.
1. Calculate the change in velocity:
- Change in velocity, Δv = Final velocity - Initial velocity = 1 m/s - 0 m/s = 1 m/s
2. Find the acceleration:
- Acceleration, a = Δv / t = 1 m/s / 1 s = 1 m/s²
3. Find the net force required:
- F_net = M * a = 75 kg * 1 m/s² = 75 N
Therefore, the force required to attain an upward speed of 1 m/s in 1 s is 75 N.
(iii) **Force required to maintain a constant speed of 1 m/s:**
Once the desired speed of 1 m/s is achieved, the force required to maintain the constant speed is determined by the equilibrium condition. According to Newton's first law of motion, an object will remain at rest or move with constant velocity unless acted upon by a net external force.
In this case, since the speed is constant, the net force acting on the system must be zero.
1. Calculate the net force required to maintain constant speed:
- F_net = 0 N
2. Find the force exerted by the painter:
- F = Weight of the system
- Weight of the system = (m₁ + m₂) * g = 75 kg * 9.8 m/s² = 735 N
Therefore, the force that should be applied by the painter to maintain a constant speed of 1 m/s is 735 N.
A 60 kg painter on a 15 kg platform. A rope attached to the platform a...
1) 2T-(M+m)g=(M+m)a M=60kg m =15kg T=400 N g=10
substituting value
a= 0.67m/s2
2) F=1/2 (M+m)(g+a)
substituting values
F=412.5N
3)
2F-(M+m)g=0
putting value
F=375 N
hope it's clear
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.