A block of mass m is pushed against a spring of constant k by a distance x. When released, it slides up a rough incline of angle theta with coefficient of friction mu. What is the maximum height reached by the block?

A. 0.5kx^2mg(1 + ) — Apply the work-energy theorem where the initial elastic potential energy equals the final gravitational potential energy plus the work done against friction. The distance along the incline is h/sin(theta), and the friction force is mu * m * g * cos(theta).

JEE Main · PhysicsHard

$A block of mass m is pushed against a spring of constant k by a distance x . When released, it slides up a rough incline of angle θ with coefficient of friction μ . What is the maximum height reached by the block?$

A. $\frac{0.5 k x ^{2}}{m g ( 1 + μ c o t θ )}$
B. $\frac{0.5 k x ^{2}}{m g ( s i n θ + μ c o s θ )}$
C. $\frac{0.5 k x ^{2}}{m g ( 1 + μ t a n θ )}$
D. $\frac{0.5 k x ^{2}}{m g s i n θ}$

Show correct answer & step-by-step solution

Correct answer: A — $\frac{0.5 k x ^{2}}{m g ( 1 + μ c o t θ )}$

Solution

Using W_{s p r in g} = Δ U_{g} + W_{f r i c t i o n}, we have 0.5 k x^{2} = m g h + μ m g cos θ (\frac{h}{s i n θ}) . Solving for h gives the result.

Attempt this question & track your score

Attempt & Track Free →

More Work Energy Power practice questions

$A force of 10 Newtons acts on a body and displaces it by 5 meters in the direction of the force. Calculate the work done$
$A body of mass 2 kg is moving with a velocity of 4 meters per second. What is its kinetic energy in Joules?$
$An object of mass 5 kg is raised to a height of 10 meters above the ground. Calculate the potential energy gained by the$
$A machine does 400 Joules of work in 20 seconds. What is the power of the machine in Watts?$
$If the velocity of a body is doubled, its kinetic energy becomes how many times its original value?$
$A p a r t i c l eo f ma ss 2 k g m o v es u n d er t h e in f l u e n ceo f a f or ce F = (3 t^{2} i + 4 t j) N . I f t h e p a r t i c l es t a r t s f r o m r es t a t$
$A block of mass 1 kg is pushed against a spring with spring constant 100 N/m, compressing it by 0.2 m. When released, th$
$A body of mass 2 kg is dropped from a height of 10 meters. Due to air resistance, it hits the ground with a speed of 12$
$A force F = (2x + 3) N acts on a particle moving along the x-axis. What is the work done by this force as the particle m$
$An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit le$
$A p a r t i c l eo f ma ss mm o v es ina p o t e n t ia l f i e l d U (x) = a / x^{2} - b / x, w h er e aan d ba r e p os i t i v eco n s t an t s . W ha t i s t h e p e$
$A block of mass m is attached to a spring of constant k and is placed on a rough horizontal surface with coefficient of$

View all Work Energy Power questions →

A block of mass m is pushed against a spring of constant k by a distance x. When released, it slides up a rough incline of angle θ with coefficient of friction μ. What is the maximum height reached by the block?

Solution

Attempt this question & track your score

More Work Energy Power practice questions

$A block of mass m is pushed against a spring of constant k by a distance x . When released, it slides up a rough incline of angle θ with coefficient of friction μ . What is the maximum height reached by the block?$