A body of mass 2 kg initially at rest moves under the action of an applied horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1. Compute the
(a) work done by the applied force in 10 s,
(b) work done by friction in 10 s,
(c) work done by the net force on the body in 10 s,
(d) change in kinetic energy of the body in 10 s, and interpret your results.
Mass of the body, m= 2 kg
Applied force, F = 7 N
Coefficient of kinetic friction, µ= 0.1
Initial velocity, u= 0
Time, t = 10 s
The acceleration produced in the body by the applied force is given by Newton's second law of motion as:
a' = F / m = 7/2 = 3.5 m/s2
Frictional force is given as:
f = µmg
= 0.1 × 2 × 9.8 = -1.96 N
The acceleration produced by the frictional force:
a'' = - 1.96 / 2 = -0.98 m/s2
Total acceleration of the body:
a = a' + a''
= 3.5 + (-0.98) = 2.52 m/s2
The distance travelled by the body is given by the equation of motion:
s = ut + ½ at2
= 0 + ½ x 2.52 x 102
= 126 m
(a) Work done by the applied force, Wa= F × s = 7 ×126 = 882 J
(b) Work done by the frictional force, Wf = F× s= -1.96 ×126 = -247 J
(c) Net force = 7 + (-1.96) = 5.04 N Work done by the net force, Wnet= 5.04 ×126 = 635 J
(d) From the first equation of motion, final velocity can be calculated as:
v = u + at = 0 + (25.2)2 ×10 = 25.2 m/s
Change in kinetic energy = 1/2 mv2 - 1/2 mu2
= ½ x 2(v2 - u2) = (25.2)2 - 02 = 635 j
State the number of significant figures in the following:
(a) 0.007 m2
(b) 2.64 x 1024 kg
(c) 0.2370 g cm-3
(d) 6.320 J
(e) 6.032 N m-2
(f) 0.0006032 m2
Fill in the blanks by suitable conversion of units:
(a) 1 kg m2s–2= ....g cm2 s–2
(b) 1 m =..... ly
(c) 3.0 m s–2=.... km h–2
(d) G = 6.67 × 10–11 N m2 (kg)–2=.... (cm)3s–2 g–1.
A physical quantity P is related to four observables a, b, c and d as follows :
The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P ? If the value of P calculated using the above relation turns out to be 3.763, to what value should you round off the result ?
Rain is falling vertically with a speed of 30 m s–1. A woman rides a bicycle with a speed of 10 m s–1 in the north to south direction. What is the direction in which she should hold her umbrella?
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(a) the total mass of the box,
(b) the difference in the masses of the pieces to correct significant figures?
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y(x,t) = 3.0 sin [36t + 0.018x + π /4]
Where x and y are in cm and t in s. The positive direction of x is from left to right.
(a) Is this a travelling wave or a stationary wave? If it is travelling, what are the speed and direction of its propagation?
(b) What are its amplitude and frequency?
(c) What is the initial phase at the origin?
(d) What is the least distance between two successive crests in the wave?
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State the number of significant figures in the following:
(a) 0.007 m2
(b) 2.64 x 1024 kg
(c) 0.2370 g cm-3
(d) 6.320 J
(e) 6.032 N m-2
(f) 0.0006032 m2
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A large steel wheel is to be fitted on to a shaft of the same material. At 27 °C, the outer diameter of the shaft is 8.70 cm and the diameter of the central hole in the wheel is 8.69 cm. The shaft is cooled using ‘dry ice’. At what temperature of the shaft does the wheel slip on the shaft? Assume coefficient of linear expansion of the steel to be constant over the required temperature range: αsteel = 1.20 x 10–5 K–1.
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x (t) = A cos (ωt + φ).
Given that at t = 0, the initial velocity of the body is ω cm/s and its initial position is 1 cm, calculate its initial phase angle and amplitude?
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x = B sin (ωt + α),
calculate the body’s amplitude and initial phase considering the initial conditions given above. [Angular frequency of the particle is π/ s]
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(Torsional spring constant α is defined by the relation J = -α ø, where J is the restoring couple and ø¸ the angle of twist).