Advertisements
Advertisements
Question
A scooter company gives the following specifications about its product:
Weight of the scooter − 95 kg
Maximum speed − 60 km/h
Maximum engine power − 3⋅5 hp
Pick up time to get the maximum speed − 5 s
Check the validity of these specifications.
Advertisements
Solution
The specifications given by the company are:
\[\text{ Mass, m = 95 kg } \]
\[\text{ Maximum power, P_m = 3 . 5 hp } \]
\[\text{ Maximum speed, v}_\text{m }= 60 \text{ km /h} \]
\[ = \frac{50}{3} \text{ m/s } \]
\[\text{ Pick up time to get maximum speed, t}_\text{m }= 5 \sec\]
So, the maximum acceleration that can be produced,
\[\text{ a }= \frac{50}{3 \times 5} = \frac{10}{3} \text{ m/ s} ^2\]
So, the driving force,
\[\text{ F = ma } = 95 \times \left( \frac{10}{3} \right)\]
\[ = \frac{950}{3} \text{ N } \]
\[\text{ Max speed, } \nu = \frac{\text{ p } }{\text{ F } }\]
\[ \Rightarrow \text{ v }=3.5\times746\times\frac{3}{950}\Rightarrow8.2 \text{ m/s } \]
As the scooter can reach a maximum of 8.2 m/s while producing a force of 950/3 N, the specifications given are not correct.
APPEARS IN
RELATED QUESTIONS
Is work-energy theorem valid in non-inertial frames?
A ball is given a speed v on a rough horizontal surface. The ball travels through a distance l on the surface and stops. What is the work done by the kinetic friction?
The US athlete Florence Griffith-Joyner won the 100 m sprint gold medal at Seoul Olympics in 1988, setting a new Olympic record of 10⋅54 s. Assume that she achieved her maximum speed in a very short time and then ran the race with that speed till she crossed the line. Take her mass to be 50 kg. Calculate the kinetic energy of Griffith-Joyner at her full speed.
A water pump lifts water from 10 m below the ground. Water is pumped at a rate of 30 kg/minute with negligible velocity. Calculate the minimum horsepower that the engine should have to do this.
An unruly demonstrator lifts a stone of mass 200 g from the ground and throws it at his opponent. At the time of projection, the stone is 150 cm above the ground and has a speed of 3 m/s. Calculate the work done by the demonstrator during the process. If it takes one second for the demonstrator to lift the stone and throw it, what horsepower does he use?
In a factory, 2000 kg of metal needs to be lifted by an engine through a distance of 12 m in 1 minute. Find the minimum horsepower of the engine to be used.
A small block of mass 200 g is kept at the top of a frictionless incline which is 10 m long and 3⋅2 m high. How much work was required (a) to lift the block from the ground and put it an the top, (b) to slide the block up the incline? What will be the speed of the block when it reaches the ground if (c) it falls off the incline and drops vertically to the ground (d) it slides down the incline? Take g = 10 m/s2.
A block weighing 10 N travels down a smooth curved track AB joined to a rough horizontal surface (In the following figure). The rough surface has a friction coefficient of 0⋅20 with the block. If the block starts slipping on the track from a point 1⋅0 m above the horizontal surface, how far will it move on the rough surface?
A particle slides on the surface of a fixed smooth sphere starting from the topmost point. Find the angle rotated by the radius through the particle, when it leaves contact with the sphere.
A particle of mass m is kept on the top of a smooth sphere of radius R. It is given a sharp impulse which imparts it a horizontal speed ν. (a) Find the normal force between the sphere and the particle just after the impulse. (b) What should be the minimum value of ν for which the particle does not slip on the sphere? (c) Assuming the velocity ν to be half the minimum calculated in part, (b) find the angle made by the radius through the particle with the vertical when it leaves the sphere.
Figure ( following ) shows a smooth track which consists of a straight inclined part of length l joining smoothly with the circular part. A particle of mass m is projected up the incline from its bottom. Find the minimum projection-speed \[\nu_0\] for which the particle reaches the top of the track.
A smooth sphere of radius R is made to translate in a straight line with a constant acceleration a. A particle kept on the top of the sphere is released at zero velocity with respect to the sphere. Find the speed of the particle with respect to the sphere as a function of the angle θ it slides.
An electron and a proton are moving under the influence of mutual forces. In calculating the change in the kinetic energy of the system during motion, one ignores the magnetic force of one on another. This is because ______.
A man, of mass m, standing at the bottom of the staircase, of height L climbs it and stands at its top.
- Work done by all forces on man is equal to the rise in potential energy mgL.
- Work done by all forces on man is zero.
- Work done by the gravitational force on man is mgL.
- The reaction force from a step does not do work because the point of application of the force does not move while the force exists.
A bullet of mass m fired at 30° to the horizontal leaves the barrel of the gun with a velocity v. The bullet hits a soft target at a height h above the ground while it is moving downward and emerges out with half the kinetic energy it had before hitting the target.
Which of the following statements are correct in respect of bullet after it emerges out of the target?
- The velocity of the bullet will be reduced to half its initial value.
- The velocity of the bullet will be more than half of its earlier velocity.
- The bullet will continue to move along the same parabolic path.
- The bullet will move in a different parabolic path.
- The bullet will fall vertically downward after hitting the target.
- The internal energy of the particles of the target will increase.
Two bodies of unequal mass are moving in the same direction with equal kinetic energy. The two bodies are brought to rest by applying retarding force of same magnitude. How would the distance moved by them before coming to rest compare?
Suppose the average mass of raindrops is 3.0 × 10–5 kg and their average terminal velocity 9 ms–1. Calculate the energy transferred by rain to each square metre of the surface at a place which receives 100 cm of rain in a year.
A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled 3 m is ______.
