A motorcycle daredevil plans to ride up a -high, ramp, sail across a -wide pool filled with hungry crocodiles, and land at ground level on the other side. He has done this stunt many times and approaches it with confidence. Unfortunately, the motorcycle engine dies just as he starts up the ramp. He is going at that instant, and the rolling friction of his rubber tires (coefficient ) is not negligible. Does he survive, or does he become crocodile food? Justify your answer by calculating the distance he travels through the air after leaving the end of the ramp.
The range is less than the width of the pool, the biker will land on the pool and hence, will not survive.
We know that the angle of inclination is , height of the inclination is , the coefficient of friction between the bike tire and the inclination surface is , width of the pool is , acceleration due to gravity and the initial speed of the bike is . We have to calculate the distance of landing position from the end of inclination.
Let's consider the information given in the question:
The equation force motion is given as
is the friction force
Substitute the values
Therefore, the length of the ramp is given as,
is the height
is the length of the ramp
Let's consider the equation of motion:
is the initial velocity
is the instant velocity
The length of the pool is .
Calculate the initial velocity has two components along the horizontal direction and the vertical direction as given as,
Therefore, the equation along the vertical direction is given as:
On solving we get,
The position of the motorcycle during the projectile time is given as,
Here we see that the distance or position of the motorcycle is less than the length of the pool. So, the motorcycle cannot cross the pool and he falls into the pool.
The distance or position of the motorcycle is 8.54m and it is less than the length of the pool. So, the motorcycle cannot cross the pool and he falls into the pool
A 100 g ball on a 60-cm-long string is swung in a vertical circle about a point 200 cm above the floor. The tension in the string when the ball is at the very bottom of the circle is 5.0 N. A
very sharp knife is suddenly inserted, as shown in FIGURE P8.56,to cut the string directly below the point of support. How far to the right of where the string was cut does the ball hit the floor?
Elm Street has a pronounced dip at the bottom of a steep hill before going back uphill on the other side. Your science teacher has asked everyone in the class to measure the radius of curvature of the dip. Some of your classmates are using surveying equipment, but you decide to base your measurement on what you’ve learned in physics. To do so, you sit on a spring scale, drive through the dip at different speeds, and for each speed record the scale’s reading as you pass through the bottom of the dip. Your data are as follows:
Scale Reading N
conical pendulum is formed by attaching a ball of mass m to a string of length L, then allowing the ball to move in a horizontal circle of radius r. FIGURE P8.47 shows that the string traces out the surface of a cone, hence the name.
a. Find an expression for the tension T in the string. b. Find an expression for the ball’s angular speed v. c. What are the tension and angular speed (in rpm) for a 500 g ball swinging in a 20-cm-radius circle at the end of a 1.0-m-long string?
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