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Find time needed for a block of mass 80 kg to slide an incline of 30 m if coefficient of friction is 0.1 and length of incline is 20 m?
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Find time needed for a block of mass 80 kg to slide an incline of 30 m...
Given Data
- Mass of block (m): 80 kg
- Length of incline (l): 20 m
- Coefficient of friction (μ): 0.1
- Distance to slide (d): 30 m
Calculating Forces
- Weight of the Block (W): W = m * g
(where g = 9.81 m/s²)
W = 80 kg * 9.81 m/s² = 784.8 N
- Normal Force (N):
N = W * cos(θ)
(Here, θ = angle of incline)
For θ = 30°, cos(30°) = √3/2 ≈ 0.866
N = 784.8 N * 0.866 ≈ 679.4 N
- Frictional Force (F_f):
F_f = μ * N
F_f = 0.1 * 679.4 N ≈ 67.94 N
Net Force Acting on the Block
- Force due to Gravity along the incline (F_g):
F_g = W * sin(θ)
sin(30°) = 0.5
F_g = 784.8 N * 0.5 = 392.4 N
- Net Force (F_net):
F_net = F_g - F_f
F_net = 392.4 N - 67.94 N = 324.46 N
Calculating Acceleration
- Acceleration (a):
a = F_net / m
a = 324.46 N / 80 kg ≈ 4.31 m/s²
Finding Time to Slide
- Using the formula:
d = (1/2) * a * t²
Rearranging gives:
t² = (2 * d) / a
t² = (2 * 30 m) / 4.31 m/s² ≈ 13.93
t ≈ √13.93 ≈ 3.73 s
Conclusion
- The time needed for the block to slide down the incline of 30 m is approximately 3.73 seconds.
- Mass of block (m): 80 kg
- Length of incline (l): 20 m
- Coefficient of friction (μ): 0.1
- Distance to slide (d): 30 m
Calculating Forces
- Weight of the Block (W): W = m * g
(where g = 9.81 m/s²)
W = 80 kg * 9.81 m/s² = 784.8 N
- Normal Force (N):
N = W * cos(θ)
(Here, θ = angle of incline)
For θ = 30°, cos(30°) = √3/2 ≈ 0.866
N = 784.8 N * 0.866 ≈ 679.4 N
- Frictional Force (F_f):
F_f = μ * N
F_f = 0.1 * 679.4 N ≈ 67.94 N
Net Force Acting on the Block
- Force due to Gravity along the incline (F_g):
F_g = W * sin(θ)
sin(30°) = 0.5
F_g = 784.8 N * 0.5 = 392.4 N
- Net Force (F_net):
F_net = F_g - F_f
F_net = 392.4 N - 67.94 N = 324.46 N
Calculating Acceleration
- Acceleration (a):
a = F_net / m
a = 324.46 N / 80 kg ≈ 4.31 m/s²
Finding Time to Slide
- Using the formula:
d = (1/2) * a * t²
Rearranging gives:
t² = (2 * d) / a
t² = (2 * 30 m) / 4.31 m/s² ≈ 13.93
t ≈ √13.93 ≈ 3.73 s
Conclusion
- The time needed for the block to slide down the incline of 30 m is approximately 3.73 seconds.
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Find time needed for a block of mass 80 kg to slide an incline of 30 m if coefficient of friction is 0.1 and length of incline is 20 m?
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Find time needed for a block of mass 80 kg to slide an incline of 30 m if coefficient of friction is 0.1 and length of incline is 20 m? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find time needed for a block of mass 80 kg to slide an incline of 30 m if coefficient of friction is 0.1 and length of incline is 20 m? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find time needed for a block of mass 80 kg to slide an incline of 30 m if coefficient of friction is 0.1 and length of incline is 20 m?.
Find time needed for a block of mass 80 kg to slide an incline of 30 m if coefficient of friction is 0.1 and length of incline is 20 m? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find time needed for a block of mass 80 kg to slide an incline of 30 m if coefficient of friction is 0.1 and length of incline is 20 m? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find time needed for a block of mass 80 kg to slide an incline of 30 m if coefficient of friction is 0.1 and length of incline is 20 m?.
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