How much work must you do to push a 13 kg block of steel across a steel table (\mu_{{\rm k}}=0.6) at a steady speed of 1.3 m/s for 2.6 s?
work= mu*mg*distance= mu*mg*v*time
To find the amount of work done to push the block of steel across the table, we need to use the formula:
Work = Force x Distance
First, let's calculate the force required to maintain a steady speed of 1.3 m/s. The force can be determined using Newton's second law of motion:
Force = Mass x Acceleration
The acceleration of the block can be calculated using the equation:
Acceleration = Net Force / Mass
The net force can be calculated using the friction between the block and the table. The frictional force can be determined using the equation:
Frictional Force = Coefficient of Friction x Normal Force
The normal force is the force exerted by the table on the block and is equal to the weight of the block, which can be calculated using:
Weight = Mass x Gravity
Given:
Mass of the block, m = 13 kg
Coefficient of friction, μk = 0.6
Speed of the block, v = 1.3 m/s
Time, t = 2.6 s
Acceleration due to gravity, g = 9.8 m/s^2
Now, let's calculate the force:
Weight = Mass x Gravity
Weight = 13 kg x 9.8 m/s^2
Weight = 127.4 N
Frictional Force = Coefficient of Friction x Normal Force
Frictional Force = 0.6 x 127.4 N
Frictional Force = 76.44 N
Acceleration = Net Force / Mass
Acceleration = Frictional Force / Mass
Acceleration = 76.44 N / 13 kg
Acceleration = 5.88 m/s^2
Now, let's calculate the distance:
Distance = Speed x Time
Distance = 1.3 m/s x 2.6 s
Distance = 3.38 m
Finally, let's calculate the work done:
Work = Force x Distance
Work = Frictional Force x Distance
Work = 76.44 N x 3.38 m
Work = 258.4392 Joules
Therefore, you would need to do approximately 258.44 Joules of work to push the 13 kg block of steel across the steel table at a steady speed of 1.3 m/s for 2.6 s.