A block of weight 2 kN is initially at rest on a rough horizontal surface (μ = 0.2). It is acted upon by a force (= P) which varies with time as shown in figure. What will be the velocity of the block at the end of 3 seconds? (assume, g = 10 m/s²)

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A block of weight 2 kN is initially at rest on a rough horizontal surface (μ = 0.2). It is acted upon by a force (= P) which varies with time as shown in figure. What will be the velocity of the block at the end of 3 seconds? (assume, g = 10 m/s²)

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1 m/s
4 m/s
2 m/s
3 m/s

Answer 1

Concept:

A block subjected to a time-varying force experiences acceleration when the applied force exceeds friction. The final velocity is calculated using Newton’s second law and kinematic equations.

Given:

Weight of block, W = 2 kN = 2000 N

Coefficient of friction, μ = 0.2

g = 10 m/s², Time = 3 s

Force applied, P = 600 N (from graph)

Calculation:

Normal reaction, N = W = 2000 N

Frictional force, \( f = \mu N = 0.2 \times 2000 = 400~N \)

Net force, \( F_{\text{net}} = 600 - 400 = 200~N \)

Mass of the block, \( m = \frac{W}{g} = \frac{2000}{10} = 200~kg \)

Acceleration, \( a = \frac{F_{\text{net}}}{m} = \frac{200}{200} = 1~m/s^2 \)

Using the kinematic equation, \( v = u + at = 0 + 1 \times 3 = 3~m/s \)

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Question

A block of weight 2 kN is initially at rest on a rough horizontal surface (μ = 0.2). It is acted upon by a force (= P) which varies with time as shown in figure. What will be the velocity of the block at the end of 3 seconds? (assume, g = 10 m/s²)

Answer (Detailed Solution Below)

Detailed Solution

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Question

A block of weight 2 kN is initially at rest on a rough horizontal surface (μ = 0.2). It is acted upon by a force (= P) which varies with time as shown in figure. What will be the velocity of the block at the end of 3 seconds? (assume, g = 10 m/s2)

Answer (Detailed Solution Below)

Detailed Solution

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A block of weight 2 kN is initially at rest on a rough horizontal surface (μ = 0.2). It is acted upon by a force (= P) which varies with time as shown in figure. What will be the velocity of the block at the end of 3 seconds? (assume, g = 10 m/s²)